Are deterministic and nondeterministic Cellular Automata equivalent?

Question

It seems that in CA context nondeterministic (ND) means probabilistic, not ND as in NFSMs. At least I haven't seen a paper or book which discusses NCAs, without talking about probabilistic CAs.

I haven't even found a definition anywhere. It feels like NCAs can't be equivalent to CAs (not in the same lattice at least), even though I can convert a NFSM to a FSM the possibly exponential growth of the required states doesn't fit to the CA definition, it would need a higher dimensional lattice (i.e. more local neighbours).

So, are NCAs and CAs equivalent ? Are there papers or books discussing this ?